You can say “a” or “an” only when you can say “one”. For example, “a chair”, “a friend”, “a CD”. Consequently, if you cannot say “one”, for example, before uncountable or plural nouns, you cannot put “a/an” before this noun.

Compare:
“I want to become a sportsman.”
“They want to become sportsmen.”

“I have bought a new CD.”
“I have bought some new CDs.”

Normally, we put “a”/”an” before new information, and “the” before the information that has already been mentioned, or we know already.

For example:
“I have a son and a daughter. The son lives at home, but the daughter is a student at university.”